Two-Dimensional Unoriented Strings And Matrix Models

TL;DR

This paper explores two-dimensional unoriented strings and superstrings, their dual matrix models, and how non-local interactions can deform oriented theories into unoriented ones, revealing integrability and duality properties.

Contribution

It introduces dual matrix models for unoriented strings, demonstrates their integrability, and shows how to deform oriented theories into unoriented ones via non-local interactions.

Findings

Dual matrix models describe renormalized unoriented string theories.

The singlet sector of the matrix models is integrable and involves Calogero-Moser interactions.

Particle-hole duality emerges in the double-scaling limit of the matrix models.

Abstract

We investigate unoriented strings and superstrings in two dimensions and their dual matrix quantum mechanics. Most of the models we study have a tachyon tadpole coming from the RP^2 worldsheet which needs to be cancelled by a renormalization of the worldsheet theory. We find evidence that the dual matrix models describe the renormalized theory. The singlet sector of the matrix models is integrable and can be formulated in terms of fermions moving in an external potential and interacting via the Calogero-Moser potential. We show that in the double-scaling limit the latter system exhibits particle-hole duality and interpret it in terms of the dual string theory. We also show that oriented string theories in two dimensions can be continuously deformed into unoriented ones by turning on non-local interactions on the worldsheet. We find two unoriented superstring models for which only oriented worldsheets contribute to the S-matrix. A simple explanation for this is found in the dual matrix model.